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Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having three or four distinct values, and new values 0..3 introduced in row major order.
1

%I #8 Jul 15 2018 12:03:46

%S 78,2520,80496,2574592,82334080,2633043200,84204544256,2692856218368,

%T 86117376515328,2754028420465408,88073659990146304,

%U 2816590245285823232,90074383313881529600,2880573254472884060928,92120556023893690612992

%N Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having three or four distinct values, and new values 0..3 introduced in row major order.

%C Column 2 of A210413.

%H R. H. Hardin, <a href="/A210407/b210407.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 31*a(n-1) + 40*a(n-2) - 280*a(n-3) + 96*a(n-4).

%F Empirical g.f.: 2*x*(39 + 51*x - 372*x^2 + 128*x^3) / (1 - 31*x - 40*x^2 + 280*x^3 - 96*x^4). - _Colin Barker_, Jul 15 2018

%e Some solutions for n=4:

%e ..0..0..1....0..0..0....0..0..0....0..1..0....0..0..0....0..0..0....0..0..0

%e ..1..2..0....1..2..1....1..2..3....2..1..2....1..2..3....1..2..1....1..2..1

%e ..0..1..2....3..2..3....0..1..2....1..0..3....3..2..1....2..3..0....1..0..0

%e ..0..3..3....1..3..0....1..3..0....2..3..1....1..0..3....1..3..1....1..2..3

%e ..0..1..0....2..1..1....0..1..3....0..0..2....3..0..1....3..0..1....3..0..3

%Y Cf. A210413.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 21 2012